A quantum version of Pollard's Rho of which Shor's Algorithm is a particular case
arxiv(2020)
Abstract
Pollard's Rho is a method for solving the integer factorization problem. The strategy searches for a suitable pair of elements belonging to a sequence of natural numbers that given suitable conditions yields a nontrivial factor. In translating the algorithm to a quantum model of computation, we found its running time reduces to polynomial-time using a certain set of functions for generating the sequence. We also arrived at a new result that characterizes the availability of nontrivial factors in the sequence. The result has led us to the realization that Pollard's Rho is a generalization of Shor's algorithm, a fact easily seen in the light of the new result.
MoreTranslated text
Key words
Pollard's Rho, Shor's algorithm, Factoring, Quantum computing, Period-finding, Order-finding
AI Read Science
Must-Reading Tree
Example
![](https://originalfileserver.aminer.cn/sys/aminer/pubs/mrt_preview.jpeg)
Generate MRT to find the research sequence of this paper
Chat Paper
Summary is being generated by the instructions you defined